单紧量子群I
Simple Compact Quantum Groups I
摘要：
引入了简单紧量子群的概念。作为非平凡的（非交换和非余交换）的例子，证明了下列紧量子群族是简单的：（a）对于$Q \in GL(n, {\mathbb C})$的泛量子群$B_u(Q)$满足$Q \bar{Q} = \pm I_n$，$n \geq 2$ ;（b）当$A_{aut}(B, τ)$，包括$n$点上的量子置换群$A_{aut}(X_n)$（$n \geq 4$）;（c）紧致李群的标准变形$K_q$ $K$及其扭曲$K_q^u$，以及Rieffel的变形$K_J$。
英文摘要：
The notion of simple compact quantum group is introduced. As non-trivial (noncommutative and noncocommutative) examples, the following families of compact quantum groups are shown to be simple: (a) The universal quantum groups $B_u(Q)$ for $Q \in GL(n, {\mathbb C})$ satisfying $Q \bar{Q} = \pm I_n$, $n \geq 2$; (b) The quantum automorphism groups $A_{aut}(B, τ)$ of finite dimensional $C^*$-algebras $B$ endowed with the canonical trace $τ$ %endowed with a tracial functional $tr$ when $\dim(B) \geq 4$, including the quantum permutation groups $A_{aut}(X_n)$ on $n$ points ($n \geq 4$); (c) The standard deformations $K_q$ of simple compact Lie groups $K$ and their twists $K_q^u$, as well as Rieffel's deformation $K_J$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
